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Bunuel
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Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at 22 Apr 2020, 05:42
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85% (hard)

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51% (02:39) correct 49% (03:16) wrong based on 134 sessions

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Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at the rate of 25 lit/min, and pipe C drains a tank at the rate of 50 lit/min. First pipe B is opened for 1 minute and then closed, after that pipe A is opened for 1 minute and then closed, after that pipe C is opened for 1 minute and then closed. If this continues till a 7000-litre empty tank is filled to the capacity, how long will it take to fill the tank ?

A. 275 minutes
B. 276 minutes
C. 277 minutes
D. 277 mins 45 sec
E. 278 minutes


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D
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Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at 24 Apr 2020, 08:59
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Bunuel
Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at the rate of 25 lit/min, and pipe C drains a tank at the rate of 50 lit/min. First pipe B is opened for 1 minute and then closed, after that pipe A is opened for 1 minute and then closed, after that pipe C is opened for 1 minute and then closed. If this continues till a 7000-litre empty tank is filled to the capacity, how long will it take to fill the tank ?

A. 275 minutes
B. 276 minutes
C. 277 minutes
D. 277 mins 45 sec
E. 278 minutes

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We see that every three minutes, the tank will be filled with 25 + 100 - 50 = 75 liters. In 92 three-minute periods (i.e., in 276 minutes), the tank will be filled with 92 x 75 = 6900 liters. When the tank is filled with 6900 liters, the next pipe that will be open is B, and since B fills the tank at the rate of 25 L/min, the tank will contain 6900 + 25 = 6925 liters at the 277th minute. Since pipe A is opened next, it will fill the remaining 7000 - 6925 = 75 liters in (75/100)*60 = 45 seconds. Therefore, the total time is 277 minutes and 45 seconds.

Answer: D
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Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at 15 Feb 2024, 08:47
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ScottTargetTestPrep

Bunuel
Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at the rate of 25 lit/min, and pipe C drains a tank at the rate of 50 lit/min. First pipe B is opened for 1 minute and then closed, after that pipe A is opened for 1 minute and then closed, after that pipe C is opened for 1 minute and then closed. If this continues till a 7000-litre empty tank is filled to the capacity, how long will it take to fill the tank ?

A. 275 minutes
B. 276 minutes
C. 277 minutes
D. 277 mins 45 sec
E. 278 minutes


 


We see that every three minutes, the tank will be filled with 25 + 100 - 50 = 75 liters. In 92 three-minute periods (i.e., in 276 minutes), the tank will be filled with 92 x 75 = 6900 liters. When the tank is filled with 6900 liters, the next pipe that will be open is B, and since B fills the tank at the rate of 25 L/min, the tank will contain 6900 + 25 = 6925 liters at the 277th minute. Since pipe A is opened next, it will fill the remaining 7000 - 6925 = 75 liters in (75/100)*60 = 45 seconds. Therefore, the total time is 277 minutes and 45 seconds.

Answer: D
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­Hi Scott, Can you please explain how you arrived at 92? I'm a little confused here. 
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Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at 15 Feb 2024, 10:04
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ss1997

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Bunuel
Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at the rate of 25 lit/min, and pipe C drains a tank at the rate of 50 lit/min. First pipe B is opened for 1 minute and then closed, after that pipe A is opened for 1 minute and then closed, after that pipe C is opened for 1 minute and then closed. If this continues till a 7000-litre empty tank is filled to the capacity, how long will it take to fill the tank ?

A. 275 minutes
B. 276 minutes
C. 277 minutes
D. 277 mins 45 sec
E. 278 minutes



 


We see that every three minutes, the tank will be filled with 25 + 100 - 50 = 75 liters. In 92 three-minute periods (i.e., in 276 minutes), the tank will be filled with 92 x 75 = 6900 liters. When the tank is filled with 6900 liters, the next pipe that will be open is B, and since B fills the tank at the rate of 25 L/min, the tank will contain 6900 + 25 = 6925 liters at the 277th minute. Since pipe A is opened next, it will fill the remaining 7000 - 6925 = 75 liters in (75/100)*60 = 45 seconds. Therefore, the total time is 277 minutes and 45 seconds.

Answer: D
­Hi Scott, Can you please explain how you arrived at 92? I'm a little confused here. 
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­The total tank capacity (7000 liters) divided by the net amount of water added per cycle (75 liters) equals approximately 93.333 cycles. In 93 cycles, netting 75 * 93 = 6975 liters added, but this includes the 50 liters removed by C in the last minute of the 93rd cycle. In 92 cycles (92 * 3 = 276 minutes), 75 * 92 = 6900 liters are added. Next, pipe B will add 25 liters making a total of 6925. Finally, 75 liters to fill the pool to capacity will be added by pipe A in 75/100 = 3/4 minutes, which is 45 seconds. Therefore, the tank will be filled in 276 + 1 + 3/4 minutes = 277 minutes and 45 seconds.
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Pipe A fills a tank at the rate of 100lit/min, Pipe B fills a tank at 17 Feb 2024, 14:10
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To solve this problem, let's calculate the net flow rate of filling or draining the tank for each minute.

Pipe B fills the tank at a rate of 25 liters/minute, so for the 1 minute it is open, it fills 25 liters.

Pipe A fills the tank at a rate of 100 liters/minute, so for the 1 minute it is open, it fills 100 liters.

Pipe C drains the tank at a rate of 50 liters/minute, so for the 1 minute it is open, it drains 50 liters.

Therefore, the net flow rate for each cycle of opening and closing the three pipes is:

Net flow rate = (25 + 100) - 50 = 75 liters/minute.

To fill a 7000-liter tank, we need to calculate how many cycles of opening and closing the three pipes are required:

7000 liters / 75 liters/minute = 93.33 minutes.

Since the time is given in minutes, we round up to the nearest whole number, which gives us 94 minutes.

However, we need to consider that the last cycle may not take a full minute if the tank becomes full before the end of that minute. In this case, we need to calculate the remaining time to fill the tank.

The remaining capacity of the tank after 93 cycles is:
7000 liters - (93 cycles * 75 liters/cycle) = 7000 - 6975 = 25 liters.

Since pipe A fills the tank at a rate of 100 liters/minute, it will take 25 liters / 100 liters/minute = 0.25 minutes to fill the remaining capacity.

Adding the remaining time to the previous time gives us:
94 minutes + 0.25 minutes = 94.25 minutes.

Therefore, it will take approximately 94.25 minutes to fill the tank.

Among the given options, the closest answer is:

D. 277 mins 45 sec.
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